/MAT/LAW117

Block Format Keyword This law represents the constitutive relation of ductile adhesive materials in 2 modes for normal and tangential directions. This law models the elastic and failure response of the material.

This material is only compatible with solid hexahedron elements (/BRICK) and the TYPE43 property (cohesive solid). This material is not compatible with any failure model. All damage and failure are defined inside of the material directly.

Format

(1)	(2)	(3)	(5)	(6)	(7)	(9)
/MAT/LAW117/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`EN`		`ET`	`I`_mass	`I`_del	`I`_rupt
`Fct_TN`	`Fct_TT`	`TN`	`TT`		`Fscale_x`
`GIC`		`GIIC`	`EXP_B`		`EXP_BK`	`Gamma`

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	(Optional) Unit Identifier. (Integer, maximum 10 digits)
`mat_title`	Material title. (Character, maximum 100 characters)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
`EN`	Stiffness normal to the plane of the cohesive element. (Real)	$[\frac{P a}{m}]$
`ET`	Stiffness in the plane of the cohesive element. (Real)	$[\frac{P a}{m}]$
`I`_mass	Mass calculation flag. = 1 (Default) Element mass is calculated using density and mean area. = 2 Element mass is calculated using density and volume. (Integer)
`I`_del	Failure flag indicating the number of integration points to delete the element (between 1 and 4). Default = 1 (Integer)
`I`_rupt	Mixed mode displacement law flag. = 1 (Default) Power law = 2 Benzeggage-Kenane (Real)
`Fct_TN`	Function identifier of the peak traction in normal direction versus element mesh size. (Integer)
`Fct_TT`	Function identifier of the peak traction in tangential direction versus element mesh size. (Integer)
`TN`	Peak traction in normal direction (default = 0) or, `Fct_TN` ordinate scale factor (default = 1) (Real)	$[Pa]$
`TT`	Peak traction in tangential direction (default = 0) or, `Fct_TT` ordinate scale factor (default = 1) (Real)	$[Pa]$
`Fscale_x`	`Fct_TN` and `Fct_TT` abscissa scale factor. Default = 1 (Real)	$[m]$
`GIC`	Energy release rate for mode I. (Real)	$[Pa . m]$
`GIIC`	Energy release rate for mode II. (Real)	$[Pa . m]$
`EXP_B`	Power law exponent for the mixed mode. Default = 2 (Real)
`EXP_BK`	Benzeggage-Kenane exponent for the mixed mode. (Real)
`Gamma`	Gamma exponent for Benzeggage-Kenane law. Default = 1 (Real)

Example (Connect Material)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
Units
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW117/1/1
CONNECT MATERIAL
#              RHO_I
              7.8E-6
#                 EN                  ET     Imass      Idel     Irupt
                   5                 1.2         0         1         0
#   Fct_TN    Fct_TT                  TN                  TT            Fscale_x
         0         0                   2                 0.7                   0
#                GIC                GIIC               EXP_B              EXP_BK               Gamma
                   1                1.75                   2                   2                   1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

Mode I refers to the normal direction and mode II refers to the shear direction. $δ_{I}$ is the separation in normal direction equal to $δ_{z z}$ direction. $δ_{I I}$ is equal to the separation in tangential direction $δ_{I I} = \sqrt{δ_{y z} + δ_{z x}}$ . The mixed mode displacement is referred to by $δ_{m}$ .
The damage initiation displacement in mode I and mode II are respectively, $δ_{I}^{0} = \frac{T_{N}}{E N}$ and $δ_{I I}^{0} = \frac{T_{T}}{E T}$ and for the mixed mode:(1)
$δ_{m}^{0} = δ_{I}^{0} \cdot δ_{I I}^{0} \cdot \sqrt{\frac{1 + β^{2}}{{(δ_{I I}^{0})}^{2} + {(β \cdot δ_{I}^{0})}^{2}}}$

With the mode mix $β = \frac{δ_{I I}}{δ_{I}}$ .
The maximum displacement at failure $δ_{m}^{F}$ can be calculated using either a Power law for I_rupt=1:(2)
$δ_{m}^{F} = \frac{2 (1 + β^{2})}{δ_{m}^{0}} \cdot {[{(\frac{E N}{G I C})}^{E X P_B} + {(\frac{β \cdot E T}{G I I C})}^{E X P_B}]}^{- (\frac{1}{E X P_B})}$

or, a Benzeggage-Kenane law for I_rupt =2:(3)
$δ_{m}^{F} = \frac{2}{δ_{m}^{0} {(\frac{1}{1 + β^{2}} \cdot E N^{γ} + \frac{β^{2}}{1 + β^{2}} \cdot E T^{γ})}^{\frac{1}{γ}}} \cdot [G I C + (G I I C - G I C) {(\frac{β^{2} \cdot E T}{E N + β^{2} \cdot E T})}^{E X P_B K}]$
GIC and GIIC are the energy release rates between the peak traction and the maximum displacement for mode I and mode II, respectively.
$G I C = \frac{T N \cdot δ_{I}^{F}}{2}$ and $G I I C = \frac{T T \cdot δ_{I I}^{F}}{2}$